Electronic Communications in Probability

On a role of predictor in the filtering stability

Pavel Chigansky and Robert Liptser

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Abstract

When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on the signal ergodic properties and the observation process regularity and may fail if either of the ingredients is ignored. In this note we address the question of stability in a particular weak sense and show that the estimates of certain functions are always stable. This is verified without dealing directly with the filtering equation and turns to be inherited from certain one-step predictor estimates.

Article information

Source
Electron. Commun. Probab., Volume 11 (2006), paper no. 13, 129-140.

Dates
Accepted: 16 July 2006
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058856

Digital Object Identifier
doi:10.1214/ECP.v11-1205

Mathematical Reviews number (MathSciNet)
MR2240706

Zentralblatt MATH identifier
1111.60022

Subjects
Primary: 93E11: Filtering [See also 60G35]
Secondary: 60J57: Multiplicative functionals

Keywords
nonlinear filtering stability martingale convergence

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Chigansky, Pavel; Liptser, Robert. On a role of predictor in the filtering stability. Electron. Commun. Probab. 11 (2006), paper no. 13, 129--140. doi:10.1214/ECP.v11-1205. https://projecteuclid.org/euclid.ecp/1465058856


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